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It is shown that the electrical breakdown mechanisms have a generic form that can exhibit deterministic chaos at sub-breakdown stresses, given a suitable parameter range. Calculation of temperature fluctuations in the thermal runaway mechanism is used to illustrate the behavior, and show the trends that may occur. Electrical tree propagation is used to outline the characteristics of deterministic chaos and to demonstrate its identification in an experimental sub-breakdown mechanism. The way in which this identification has been used to guide the development of a deterministic physical model for tree propagation is discussed. Some speculations are also made as to the possibility of using the properties of deterministic chaos for prediction, and on the relationship of deterministic chaos to cessation of activity prior to failure.